Importance Measures for a Binary State System

The performance evaluation of a system having n identical units, each of which consists of two components has been successfully discussed in binary-state reliability analysis. In this paper, we study the performance evaluation of a multi-state system based on bivariate order statistics. The multi-state system consists of n independent and identical units, each having two components. The components of each unit are assumed to be s-dependent. However, the units work s-independently with each other. The system and each component of each unit having three performance levels “0 (failure), 1 (partially working) and 2 (completely working)” are considered. The degradation of the components follows Markov Process and also Farlie-Gumbel-Morgenstern distribution is used to model the s-dependence of the components. The reliability analysis of a multi-state k-out-of- n system are evaluated under the assumptions. Some dynamic performance measures for the system such as the mean residual and mean past lifetime functions based on bivariate order statistics are also evaluated. The performance of the system is especially examined for different values of s-dependence parameter, the degradation rates and different number of units for the system. The results are supported with some numerical examples and graphical representations.

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On the multi-state signatures of ordered system lifetimes

Advances in Applied Probability ◽

10.1017/apr.2019.65 ◽

2020 ◽

Vol 52 (1) ◽

pp. 291-318 ◽

Cited By ~ 3

Author(s):

He Yi ◽

Narayanaswamy Balakrishnan ◽

Lirong Cui

Keyword(s):

State System ◽

Coherent System ◽

Life Test ◽

Binary State

AbstractIn this paper, the signature of a multi-state coherent system with binary-state components is discussed, and then it is extended to the case of ordered system lifetimes arising from a life-test on coherent multi-state systems with the same multi-state system signature. Some properties of the multi-state system signature and the ordered multi-state system signature are also studied. The results established here are finally explained through some illustrative examples.

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Reliability analysis and selective maintenance for multistate queueing system

Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability ◽

10.1177/1748006x211034326 ◽

2021 ◽

pp. 1748006X2110343

Author(s):

Tang Tang ◽

Lijuan Jia ◽

Jin Hu ◽

Yue Wang ◽

Cheng Ma

Keyword(s):

Queueing System ◽

Operation Time ◽

State System ◽

Profit Rate ◽

Time Service ◽

Queueing Process ◽

System A ◽

Binary State ◽

Deterioration Process ◽

Selective Maintenance

The reliability theory of the multi-state system (MSS) has received considerable attention in recent years, as it is able to characterize the multi-state property and complicated deterioration process of systems in a finer way than that of binary-state system. In general, the performance of the task processing type MSS is typically measured by an operation time (processing speed). Whereas, considering the queueing phenomenon caused by the random arrival and processing of tasks, some other criteria should be taken into account to evaluate the quality of service (QoS) and the profit of stakeholders, such as waiting time, service and abandon rate of tasks and consequent profit rate. In this article, we focus on the queueing process of tasks and analyse the performance and reliability of MSS in an M/M/2 queueing model, which is referred to as a multi-state queueing system (MSQS). Two kinds of deterioration are studied including the gradual degradation of servers and the sudden breakdown of the whole system. A performance assessment function is defined to obtain the profit rate of MSQS in different performance states. Based on the proposed performance function, the selective maintenance method is studied to optimize the accumulated profit under the constraint of maintenance resource and time.

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A generalized model selection framework for multi-state failure data analysis

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-08-2021-0280 ◽

2022 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Rajkumar Bhimgonda Patil ◽

Suyog Subhash Patil ◽

Gajanand Gupta ◽

Anand K. Bewoor

Keyword(s):

Data Analysis ◽

Reliability Analysis ◽

State System ◽

Numerical Control ◽

Failure Behavior ◽

Class Iii ◽

Content Type ◽

Failure Data ◽

Binary State ◽

Design Attribute

PurposeThe purpose of this paper is to carry out a reliability analysis of a mechanical system considering the degraded states to get a proper understanding of system behavior and its propagation towards complete failure.Design/methodology/approachThe reliability analysis of computerized numerical control machine tools (CNCMTs) using a multi-state system (MSS) approach that considers various degraded states rather than a binary approach is carried out. The failures of the CNCMT are classified into five states: one fully operational state, three degraded states and one failed state.FindingsThe analysis of failure data collected from the field and tests conducted in the laboratory provided detailed understandings about the quality of the material and its failure behavior used in designing and the capability of the manufacturing system. The present work identified that Class II (major failure) is critical from a maintainability perspective whereas Class III (moderate failure) and Class IV (minor failure) are critical from a reliability perspective.Research limitations/implicationsThis research applies to reliability data analysis of systems that consider various degraded states.Practical implicationsMSS reliability analysis approach will help to identify various degraded states of the system that affect the performance and productivity and also to improve system reliability, availability and performance.Social implicationsIndustrial system designers recognized that reliability and maintainability is a critical design attribute. Reliability studies using the binary state approach are insufficient and incorrect for the systems with degraded failures states, and such analysis can give incorrect results, and increase the cost. The proposed MSS approach is more suitable for complex systems such as CNCMT rather than the binary-state system approach.Originality/valueThis paper presents a generalized framework MSS's failure and repair data analysis has been developed and applied to a CNCMT.

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